Up or down day is not important in this buy-write scenario IMO. You want to open the position at as high IV as possible to maximize returns on the call sale. Shares cost the same no matter the IV.
I agree with the details, but not the conclusion.
My rationale for buy-write at relatively low share price (down day) is that I want a regression that takes me above the short strike, and a close for the strike to strike gain plus the opening credit.
The reason I optimize that way is that strike to strike changes in the share price tend to overwhelm the short call credits.
Note that despite my rationale for buy-write on a down day / relatively low share price, my buy-writes I did today are on an up day. I clearly don't feel strongly about these on a down day
A recent experience - the day that shares hit 1150 recently, I made a decision that day that I needed to sell some shares to reach my target cash %. Shares were 1133 at the time and I decided to sell.
I did that sale in the form of an 1100 strike cc ($48 credit), figuring that at anything over 1100 I'd get the 1133 I wanted plus another $15 for the privilege. Then the shares dropped down to 1080 before expiration. I kept the $45 net - that was nice. I could be rebuying those shares today at $680; would have rebought around 830. I've had no chance to sell enough cc to have captured the $300(+) strike to strike benefit that was available has I just sold the shares.
Of course I didn't know that, but the thing is - I had decided to sell the shares. It was time, the cash % was too low for my own discipline and trading approach, and I got greedy. Note that I'm not really lamenting the outcome - one benefit is that I didn't need to decide later when to buy back in. Nor did I know if there would be a good future option to buy back in.
But my trading strategy demand this of me (I always maintain 50%+ account value in shares, so I have lots of exposure to breakouts), and I didn't carry through. That is the real problem
With a buy-write, the purchase price of the shares does matter. Had I executed a buy-write at 1133, selling the 1100 call, looking to earn $18 in 3 or 4 days, and then continued selling cc to today, then I'd be looking at something like a $450 strike to strike (unrealized) loss while having collected maybe $100 in cc gains. To reach a strike to strike gain I'd be (and am) selling pretty far OTM calls, with the hope that I'll be able to roll far enough, fast enough, to get back to a neutral strike to strike position.